The above automated selection of active orbitals is clearly different from the atomic valence active space (AVAS) approach[1]}, where the \(K\)  valence AOs are used to select both the occupied and unoccupied active orbitals,
thereby leading to in total \(2K\)  active orbitals. The number of rotated active orbitals can be reduced therein by discarding those with small singular values but then there is no guarantee to
maintain the same CAS for all geometries of complex systems.
In contrast, the \(K\)  AOs (which may include core AOs) are separated here into doubly, singly and zero occupied ones, which are then used as probes to select
the corresponding active orbitals.
The number of the so-selected active orbitals is hence just \(K\)  instead of \(2K\) . This is precisely the spirit of F2M[2]}. As a matter of fact, some pFLMOs from
subsystems calculations[3]} can also be used to form the (global) pre-LMOs. This way, the task of selecting active orbitals for a large system is split into selections of
subsystem active orbitals. If wanted, the number of active orbitals can be reduced by first semicanonicalizing those pre-LMOs of a fragment (e.g., an aromatic ring; cf. (REF )) and then picking up
those of right “energies” (NB: semicanonicalization means here that the doubly, singly and zero occupied pre-LMOs
are canonicalized separately). Since such regional pre-CMOs are still localized on the chosen fragment, they can be used simply as pre-LMOs, provided that the molecular LMOs localized on the same fragment
are also semicanonicalized in the same way. The CAS will remain the same for all geometries as long as the chosen fragments maintain their characters. A similar idea was also adopted by the PiOS apprach[4]} but only for \(\pi \) -orbital spaces (PiOS)
of aromatic rings, as implied by the acronym. Alternatively, one can define several local active spaces (LAS)[5]} and further impose certain restrictions on the excitations between the LASs, as illustrated in Fig. REF .
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